Variable Selection of Single-Index Quantile Regression

Nonparametric quantile regression with multivariate covariates is a difficult estimation. To reduce the dimensionality while still retaining the flexibility of nonparametric model, the single-index regression is often used to model the conditional quantile of a response variable. In this paper, we focus on the variable selection aspect of single-index quantile regression. Based on the minimized average loss estimation (MALE), the variable selection is done by minimizing the average loss with SCAD penalty. Under some mild conditions, we demonstrate the oracle properties about SCAD variable section of single-index quantile regression. Furthermore, the algorithm of the variable selection of SCAD penalized quantile regression is given. Some simulations are done to illustrate the performance of the proposed methods.